Model order reduction for the cross-diffusive Brusselator Equation
Departments of Mathematics, Balıkesir University, Çağıs Campus, 10145 Balıkesir, Turkey.
Research Article
GSC Advanced Research and Reviews, 2024, 21(02), 373–381.
Article DOI: 10.30574/gscarr.2024.21.2.0452
Publication history:
Received on 14 October 2024; revised on 21 November 2024; accepted on 23 November 2024
Abstract:
The cross-diffusive Brusselator equation is a reaction-diffusive system that models complex chemical and biological process with both self-diffusion and cross-diffusion effects. These equations exhibit rich spatiotemporal dynamics, including Turing patterns and instability-driven pattern formations. Despite its significance, the computational cost of solving high-dimensional discretized versions of the cross-diffusive Brusselator equation can be prohibitive, particularly in parameter-dependent or long-time simulations. This study presents a model order reduction (MOR) framework tailored to the Brusselator equation, leveraging Proper Orthogonal Decomposition (POD) combined with Galerkin projection along with the Discrete Empirical Interpolation Method (DEIM) and the Dynamic Mode Decomposition Method (DMD) to efficiently approximate nonlinear dynamics. The reduced models are constructed to preserve key features of the original system, including stability and accuracy, while achieving substantial computational savings. Numerical experiments validate the proposed approach, demonstrating its effectiveness in capturing the essential dynamics of the Brusselator equation under various parameter settings. These findings provide a robust pathway for efficient simulation and analysis of reaction-diffusion systems in scientific and engineering applications.
Keywords:
Model Order Reduction; Cross-Diffusive Brusselator Equation; Proper Orthogonal Decomposition; Discrete Empirical Interpolation Method; Dynamic Mode Decomposition; Reaction-Diffusion Systems; Computational Efficiency
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Copyright © 2024 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0
